Numerical boundary conditions in Finite Volume and Discontinuous Galerkin schemes for the simulation of rarefied flows along solid boundaries

Céline Baranger (1) , Nicolas Hérouard (2) , Julien Mathiaud (1) , Luc Mieussens (3, 2)

1 CESTA - Centre d'études scientifiques et techniques d'Aquitaine
2 IMB - Institut de Mathématiques de Bordeaux
3 CARDAMOM - Certified Adaptive discRete moDels for robust simulAtions of CoMplex flOws with Moving fronts

We present a numerical comparison between two standard finite volume schemes and a discontinuous Galerkin method applied to the BGK equation of rarefied gas dynamics. We pay a particular attention to the numerical boundary conditions in order to preserve the rate of convergence of the method. Most of our analysis relies on a 1D problem (Couette flow), but we also present some results for a 2D aerodynamical flow.

Mots clés: BGK model; Numerical boundary conditions; Finite Volume Schemes; Discontinuous Galerkin schemes; discrete velocity model; transitional regime; rarefied flow simulation

Domaines: Analyse numérique [math.NA]; Mécanique des fluides [physics.class-ph]

Céline Baranger, Nicolas Hérouard, Julien Mathiaud, Luc Mieussens. Numerical boundary conditions in Finite Volume and Discontinuous Galerkin schemes for the simulation of rarefied flows along solid boundaries. 2018. ⟨hal-01552756v3⟩